By David Bergamini. New York: Time, 1963. 200 pages.
Mathematics by David Bergamini, an entry in Time’s “Life Science Library,” is a dated yet still useful survey of mathematics for the casual reader. Major news papers and magazines across the United States are cutting back their science coverage, and often those whom they have reporting on scientific matters have little background in the sciences. Furthermore, many great popularizers of science, such as Isaac Asimov and Carl Sagan, have passed away in recent years. What is true of the natural sciences is unfortunately even more true of mathematics.
For this reason it is quite reasonable to recommend such an older work. Indeed, though Bergamini’s volume was first published in 1963, it was a book that I read in elementary and middle school in the 1980s, and it is likely to be a book that many school and public libraries still have in their collections.
Bergamini’s book is divided into eight evenly-sized chapters, each of which proceeds mostly chronologically through a variety of topics. Chapter One covers the concept of numbers, a variety of numbering and counting systems, and works its way toward modern computers. Chapter Two should be two chapters; it begins with a survey of Greek mathematics, focusing on geometry, and then shifts gears to present a portfolio of “Eminent Masters of Mathematics.” After this, however, the book really hits its stride with sections on the mathematics—particularly algebra—of ancient cultures (Chapter Three), curves and math in nature (Chapter Four), movement and calculus (Chapter Five), and probability and chance (Chapter Six).
The seventh chapter, entitled “A Logical Leap into the Wild Blue Yonder,” is a bit like the second in that its focus is geometry, but this time it is not Euclid and the Greeks, but rather Gauss, Riemann, and Einstein who form the chapter’s core, and it is this progression through the chapters—from numbers, plane geometry, calculus, probability, and back to geometry—that is wrapped up in the eighth and final chapter. Here the author surveys comprehensible yet interesting results in topology, graph theory, and set theory. The general trend in the book is from the concrete and everyday to the more abstract—accompanied by numerous visual aids—and this form of presentation makes even the most counter-intuitive of the results easily accessible.
With its large, hardcover format, numerous graphs, color photos, and illustrations, Bergamini’s Mathematics is a general math reference that, while several decades old and out-of-print, is still a useful resource for casual readers, inquisitive children, and even primary & secondary school teachers who are interested in the magic, beauty, and fun of mathematics. The book’s faults, such as its lack of coverage of female mathematicians, and its ignorance of current trends and fads (chaos theory and fractals, game theory, etc.), are results of its age. This reviewer recommends Bergamini’s volume as a stepping stone to some of the fascinating and more specialized popular-math books that have appeared in recent years on such topics as fractals and chaos, pi, and zero/nothingness.